When engaged in a discussion or debate, there are many different ways to express the idea of the "course of argument." Some synonyms might include the "trajectory of the conversation," "line of reasoning," or "path of dialogue." Other possible options might include "flow of discourse," "progression of thought," or "evolution of the discussion." Ultimately, the most appropriate synonym to use will depend on the specific context in which the discussion or debate is taking place and the tone or style of the communication being used. Regardless of the specific word choice, however, all of these synonyms serve to convey the idea of the direction and momentum of the conversation.